What's wrong with my node setup for PBR materials?
1) What's wrong with my nodes?

There is no real reason to solely use a Diffuse shader. Virtually all materials have gloss, so you should either mix a diffuse and a gloss or use Principled BSDF.

2) How to hook displacement into nodes?

Turn on the Experimental feature set (can be found under the "Render" button). Go to your material settings and under "Settings" change from Bump to True. Then plug in your displacement map (you may need some math nodes to get a good looking result). Also consider using adaptive subdivision to ensure you have enough geometry to displace.

3) What is the purpose of Texture Coordinates and Mapping?

The texture coordinates tell your material what coordinates your textures should use—generated coordinates, the UV map, etc. The mapping node can be used to scale, rotate, or move your texture around independent of the texture coordinates.